Simplify; express your answer in exponential form. Assume $p\neq 0, n\neq 0$. $\dfrac{{p}}{{(p^{-5}n^{3})^{-5}}}$
Answer: To start, try working on the numerator and the denominator independently. In the numerator, we have ${p}$ to the exponent ${1}$ . Now ${1 \times 1 = 1}$ , so ${p = p}$ In the denominator, we can use the distributive property of exponents. ${(p^{-5}n^{3})^{-5} = (p^{-5})^{-5}(n^{3})^{-5}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{p}}{{(p^{-5}n^{3})^{-5}}} = \dfrac{{p}}{{p^{25}n^{-15}}}$ Break up the equation by variable and simplify. $\dfrac{{p}}{{p^{25}n^{-15}}} = \dfrac{{p}}{{p^{25}}} \cdot \dfrac{{1}}{{n^{-15}}} = p^{{1} - {25}} \cdot n^{- {(-15)}} = p^{-24}n^{15}$.